WASHINGTON—The number of people seeking first-time jobless benefits fell for the third consecutive week, though the overall level of claims suggests that the labor market is improving only slowly.

Initial claims for unemployment benefits, a measure of layoffs, declined by 10,000 to a seasonally adjusted 340,000 in the week ended Oct. 26, the Labor Department said Thursday. Economists surveyed by Dow Jones had expected 335,000 new...